An Introduction to the Finite Element Method for Differential Equations /
"The objective of this book is two-fold. The first objective is to construct, as much as possible, stable finite element schemes without affecting accuracy. The second objective is to derive convergence of the numerical schemes up to maximal available regularity of the exact solution. The first...
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| Format: | text |
| Language: | eng |
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Hoboken, NJ : Wiley,
2021
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| _version_ | 1796762666472046592 |
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| author | Mohammad Asadzadeh, author 639196 |
| author_facet | Mohammad Asadzadeh, author 639196 |
| author_sort | Mohammad Asadzadeh, author 639196 |
| collection | OCEAN |
| description | "The objective of this book is two-fold. The first objective is to construct, as much as possible, stable finite element schemes without affecting accuracy. The second objective is to derive convergence of the numerical schemes up to maximal available regularity of the exact solution. The first two chapters of the book cover existence, uniqueness and stability as well as the working environment, such as vector and function spaces and principle mathematical inequalities. Chapters 3 and 4 cover the approximation procedure with piecewise linears, interpolation, numerical integration and numerical solution of linear system of equations. Chapters 5 through 7 are devoted to the finite element approximations for the one-space dimensional, boundary value problems, initial value problems, and initial-boundary value problems. Finally, Chapters 8 through 10 are an extension of Chapters 3 and 5-7 to higher spatial dimensions. This book is a great resource for upper undergraduates and graduates in applied math, engineering and natural sciences, as well as researchers in industry and academia in need of finite element approximation techniques. Researchers in industry and academia in need of finite element approximation techniques. Some advanced classes in second year."-- |
| first_indexed | 2024-03-05T16:44:13Z |
| format | text |
| id | KOHA-OAI-TEST:592903 |
| institution | Universiti Teknologi Malaysia - OCEAN |
| language | eng |
| last_indexed | 2024-03-05T16:44:13Z |
| publishDate | 2021 |
| publisher | Hoboken, NJ : Wiley, |
| record_format | dspace |
| spelling | KOHA-OAI-TEST:5929032022-02-14T01:54:29ZAn Introduction to the Finite Element Method for Differential Equations / Mohammad Asadzadeh, author 639196 textHoboken, NJ : Wiley,2021©2021eng"The objective of this book is two-fold. The first objective is to construct, as much as possible, stable finite element schemes without affecting accuracy. The second objective is to derive convergence of the numerical schemes up to maximal available regularity of the exact solution. The first two chapters of the book cover existence, uniqueness and stability as well as the working environment, such as vector and function spaces and principle mathematical inequalities. Chapters 3 and 4 cover the approximation procedure with piecewise linears, interpolation, numerical integration and numerical solution of linear system of equations. Chapters 5 through 7 are devoted to the finite element approximations for the one-space dimensional, boundary value problems, initial value problems, and initial-boundary value problems. Finally, Chapters 8 through 10 are an extension of Chapters 3 and 5-7 to higher spatial dimensions. This book is a great resource for upper undergraduates and graduates in applied math, engineering and natural sciences, as well as researchers in industry and academia in need of finite element approximation techniques. Researchers in industry and academia in need of finite element approximation techniques. Some advanced classes in second year."--Includes bibliographical references and index.1 Introduction -- 2 Mathematical Tools -- 3 Polynomial Approximation/Interpolation in 1d -- 4 Linear Systems of Equations -- 5 Two-Point Boundary Value Problems -- 6 Scalar Initial Value Problems -- 7 Initial Boundary Value Problems in 1d -- 8 Approximation in Several Dimensions -- 9 The Boundary Value Problems in ℝN -- 10 The Initial Boundary Value Problems in ℝN -- Appendix A Answers to Some Exercises -- Appendix B Algorithms and Matlab Codes -- Appendix C Sample Assignments -- Appendix D Symbols."The objective of this book is two-fold. The first objective is to construct, as much as possible, stable finite element schemes without affecting accuracy. The second objective is to derive convergence of the numerical schemes up to maximal available regularity of the exact solution. The first two chapters of the book cover existence, uniqueness and stability as well as the working environment, such as vector and function spaces and principle mathematical inequalities. Chapters 3 and 4 cover the approximation procedure with piecewise linears, interpolation, numerical integration and numerical solution of linear system of equations. Chapters 5 through 7 are devoted to the finite element approximations for the one-space dimensional, boundary value problems, initial value problems, and initial-boundary value problems. Finally, Chapters 8 through 10 are an extension of Chapters 3 and 5-7 to higher spatial dimensions. This book is a great resource for upper undergraduates and graduates in applied math, engineering and natural sciences, as well as researchers in industry and academia in need of finite element approximation techniques. Researchers in industry and academia in need of finite element approximation techniques. Some advanced classes in second year."--PSZ_JBFinite element methodDifferential equationsURN:ISBN:9781119671640 |
| spellingShingle | Finite element method Differential equations Mohammad Asadzadeh, author 639196 An Introduction to the Finite Element Method for Differential Equations / |
| title | An Introduction to the Finite Element Method for Differential Equations / |
| title_full | An Introduction to the Finite Element Method for Differential Equations / |
| title_fullStr | An Introduction to the Finite Element Method for Differential Equations / |
| title_full_unstemmed | An Introduction to the Finite Element Method for Differential Equations / |
| title_short | An Introduction to the Finite Element Method for Differential Equations / |
| title_sort | introduction to the finite element method for differential equations |
| topic | Finite element method Differential equations |
| work_keys_str_mv | AT mohammadasadzadehauthor639196 anintroductiontothefiniteelementmethodfordifferentialequations AT mohammadasadzadehauthor639196 introductiontothefiniteelementmethodfordifferentialequations |